13 original questions, 49 marks. Type your answers below for an instant mark and a score (algebra in any equivalent form, e.g. 2sqrt(3) or 2√3), or print the worksheet, mark it with the answers sheet, and use the solutions to see every step written out by hand.
The diagram shows five quadrilaterals, labelled A, B, C, D and E, drawn on a centimetre grid.
Here is some information about four pairs of triangles.
For each pair, write down the condition (SSS, SAS, ASA or RHS) that shows the triangles are congruent, or write "not necessarily congruent".
PQRS is a parallelogram.
Angle P = (3x + 15)° and angle Q = (2x − 10)°. Angles P and Q are next to each other on the same side of the parallelogram.
Work out the value of x. Give a reason for each stage of your working.
AB and CD are parallel lines. The line PQ crosses them at P and Q.
One of the angles at P is 62°, as shown.
AB and CD are parallel straight lines.
A straight line crosses AB at E and crosses CD at F. On line AB, A is to the left of E and B is to the right of E. On line CD, C is to the left of F and D is to the right of F.
Angle AEF = 62°.
Work out the size of angle CFE.
Give a reason for each stage of your working.
PQR is a triangle. The side PQ is extended to the point S.
Angle RQS = 112° and angle QPR = 44°.
Show that triangle PQR is isosceles. Give a reason for each stage of your working.
ABC is a triangle. The side BC is extended to the point D.
Angle BAC = a and angle ABC = b.
Prove that angle ACD = a + b.
Give a reason for each stage of your working.
ABCDEF is a hexagon.
Angle A = angle D = 90°.
The other four interior angles are all equal.
Work out the size of angle B.
AB and CD are parallel straight lines. A straight line crosses them both.
Two co-interior angles between the parallel lines are (3x + 20)° and (2x − 15)°.
Work out the size of the smaller of these two angles.
You must show all your working.
In triangle ABC, AB = AC.
The point D lies on BC so that AD bisects angle BAC.
Prove that triangle ABD is congruent to triangle ACD.
AB and CD are parallel straight lines, with AB above CD.
E lies on AB and G lies on CD. F is a point between the two lines, to the right of both E and G, so that EFG forms a zigzag.
Angle BEF = 38° and angle DGF = 44°, where B is to the right of E and D is to the right of G.
Work out the size of angle EFG.
Give a reason for each stage of your working.
Extension questions: beyond the core Year 9 objectives, for pupils who want a stretch.
ABCDEF is a regular hexagon. ABGH is a square.
The hexagon and the square have the same side length and share the side AB.
F is joined to H.
Give a reason for each stage of your working.
Answer the questions above and your score appears here.
Every question here is original and written by Robinson Tuition. It follows the Key Stage 3 programme of study; Year 9 sheets end with extension questions for top sets.